The present disclosure relates generally to systems and methods for dimension reduction for multivariable extremum-seeking optimization. Extremum-seeking optimization is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. Modern systems often have a myriad of inputs that can be manipulated in order to optimize the performance index. Control techniques that manipulate many variables simultaneously can offer superior performance over those that divide a system into separate single variable control loops. Because complexity and computational load may increase exponentially with the number of manipulated variables, a subset of variables p is chosen from the total possible number n of variables (p<n) in setting up the multivariable control or optimization. Conventional approaches for selecting the subset of variables p range from rules of thumb to detailed system identification experiments. Generally, the conventional approaches involve making a binary decision for each possible variable as to whether to include the variable in the control or optimization. Thresholds of some sort are thus needed in order to make the binary decisions on variable inclusion, which can be difficult to determine. A more applicable approach for reducing the dimensionality of a control or optimization problems is therefore desired.